Parallel velocity shear instabilities in an inhomogeneous plasma with a sheared magnetic field

Injection of fast neutrals with a component of the beam velocity along the magnetic field

B_{0}

results in a plasma having a sheared mean velocity along

B_{0}

. If this parallel velocity shear

U′

and the density inhomogeneity scale length

L_{n}

are large enough so that

{U ′|L}_{n} {|/(τ + 1)}^{1/2} υ_{i} > 1

then a parallel Kelvin‐Helmholtz instability is excited, where

v_{i}

is the ion thermal speed and

τ

is the electron temperature/ion temperature. Magnetic shear stabilization requires a shear length

L_{s}

comparable to or less than

{|L}_{n} |

, namely,

{τL}_{s} {/3 (τ + 1) < υ}_{i} {/U ′ < |L}_{n} {|/(τ + 1)}^{1/2}

. For

{U ′|L}_{n} {|/(τ + 1)}^{1/2} υ_{i} < 1

, however, this parallel Kelvin‐Helmholtz instability is stabilized and only drift wave instabilities can be excited. For

τ ≈ 1

and

{(M / m)}^{1/2} ≈ 43

, the first of these drift wave instabilities is unstable for

{U ′/Ω}_{i} {> 172| (L}_{n} {/ L}_{s})^{3/2} |

provided

{|L}_{n} {/L}_{s} {| < a}_{i} {/30|L}_{n} |

, while the second is stable for

{U ′ /Ω}_{i} {< 136a}_{i} {/|L}_{s} |

provided

{|L}_{s} {/L}_{n} | > 600

and

{U ′ /Ω}_{i} ≪ 1

, where

a_{i}

and

Ω_{i}

are the ion gyration radius and frequency.

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